My current research in mathematical physics deals with employing weak and strong deflection gravitational lensing to test theories
of gravity, explore the geometry of spacetime around black holes, and probe
the nature of dark matter on galactic scales.
I utilize tools from astrophysics, cosmology, general relativity, high energy physics, and a variety of mathematical fields
(e.g., differential geometry, singularities, and probability theory). A mathematical theory of gravitational lensing is presented in the
Singularity Theory and Gravitational Lensing (A. O. Petters, H. Levine, and J. Wamsbganss).
I am co-authoring a two-volume text on Mathematical Finance. In addition, I am
involved with Entrepreneurship
and Innovation in Science and Technology for the Developing World.
are being piloted in Belize in collaboration with the
and through my joint appointment with Duke's Fuqua School of Business.
The overall goal is to research and implement
innovative ways to drive national
development through high-tech industries.